Multiple-scale perturbation method on integro-differential equations: Application to continuous-time quantum walks on regular networks in non-Markovian reservoirs

Meng, Xiangyi; Li, Yang; Zhang, Jianwei; Guo, Hong; Stanley, H. Eugene

doi:10.1103/physrevresearch.1.023020

Cited by 5 publications

(4 citation statements)

References 45 publications

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“…The discussion of this phenomenon for some other physical models could be found in [63]. The singularity of the perturbation theory here coincides with [64], where multiple-scale singular perturbation theory was used for open quantum systems.…”

Section: Introductionmentioning

confidence: 63%

Non-perturbative effects in corrections to quantum master equations arising in Bogolubov–van Hove limit

Teretenkov¹

2021

J. Phys. A: Math. Theor.

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We study the perturbative corrections to the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) equation which arises in the weak coupling limit. The spin-boson model in the rotating wave approximation at zero temperature is considered. We show that the perturbative part of the density matrix satisfies the time-independent GKSL equation for arbitrary order of the perturbation theory (if all the moments of the reservoir correlation function are finite). But to reproduce the right asymptotic precision at long times, one should use an initial condition different from the one for exact dynamics. Moreover, we show that the initial condition for this master equation even fails to be a density matrix under certain resonance conditions.

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Section: Introductionmentioning

confidence: 63%

Non-perturbative effects in corrections to quantum master equations arising in Bogolubov–van Hove limit

Teretenkov¹

2021

J. Phys. A: Math. Theor.

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“…The multiple-scales method [23][24][25][26] has wide-ranging applications throughout physics [27][28][29]. For instance, the Chapman-Enskog expansion, used in derivations of the Navier-Stokes equations from the Boltzmann equation relies on it (see, e.g., [30]), as well as any homogenisation technique used to study diffusion or transport processes in inhomogeneous media [26].…”

Section: The Methods Of Multiple Scalesmentioning

confidence: 99%

Multiple-scales approach to the averaging problem in cosmology

Ginat

2021

J. Cosmol. Astropart. Phys.

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The Universe is homogeneous and isotropic on large scales, so on those scales it is usually modelled as a Friedmann-Lemaítre-Robertson-Walker (FLRW) space-time. The non-linearity of the Einstein field equations raises concern over averaging over small-scale deviations form homogeneity and isotropy, with possible implications on the applicability of the FLRW metric to the Universe, even on large scales. Here I present a technique, based on the multiple-scales method of singular perturbation theory, to handle the small-scale inhomogeneities consistently. I obtain a leading order effective Einstein equation for the large-scale space-time metric, which contains a back-reaction term. The derivation relies on a series of consistency conditions, that ensure that the growth of deviations from the large-scale space-time metric do not grow unboundedly; criteria for their satisfiability are discussed, and it is shown that they are indeed satisfied if matter is non-relativistic on small scales. The analysis is performed in harmonic gauge, and conversion to other gauges is discussed. I estimate the magnitude of the back-reaction term relative to the critical density of the Universe in the example of an NFW halo, and find it to be of the order of a few percent. In this example, the back-reaction term is interpreted as a contribution of the energy-density of gravitational potential energy, averaged over the small-scale, to the total energy-momentum tensor.

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“…The multiple-scales method [23][24][25][26] has wide-ranging applications throughout physics [27][28][29]; for instance, the Chapman-Enskog expansion, used in deriving the Navier-Stokes equations from the Boltzmann equation relies on it (see, e.g., [30]), as well as any homogenisation technique used to study diffusion or transport processes in inhomogeneous media [26].…”

Section: A the Methods Of Multiple Scalesmentioning

confidence: 99%

Multiple-Scales Approach to The Averaging Problem in Cosmology

Ginat

2020

Preprint

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The Universe is homogeneous and isotropic on large scales, so on those scales it is usually modelled as a Friedmann-Lemaître-Robertson-Walker (FLRW) space-time.The non-linearity of the Einstein field equations raises concern over averaging over small-scale deviations form homogeneity and isotropy, with possible implications on the applicability of the FLRW metric to the Universe, even on large scales. Here I present a technique, based on the multiple-scales method of singular perturbation theory, to handle the small-scale inhomogeneities consistently. I obtain a leading order effective Einstein equation for the large-scale space-time metric, which contains a back-reaction term. The derivation of this equation is done in harmonic gauge, and conversion to other gauges is discussed. I estimate the magnitude of the backreaction term relative to the critical density of the Universe in an example, and find it to be of the order of a few percent.

show abstract

Multiple-scale perturbation method on integro-differential equations: Application to continuous-time quantum walks on regular networks in non-Markovian reservoirs

Cited by 5 publications

References 45 publications

Non-perturbative effects in corrections to quantum master equations arising in Bogolubov–van Hove limit

Non-perturbative effects in corrections to quantum master equations arising in Bogolubov–van Hove limit

Multiple-scales approach to the averaging problem in cosmology

Multiple-Scales Approach to The Averaging Problem in Cosmology

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